The Blow-Up Behavior of the Heat Equation with Neumann Boundary Conditions - Deng, K. (Journal of mathematical analysis and applications, 1994)
We establish the blow-up rate for the solution of the heat equation u t = u xx , 0 < x < 1, t > 0 subject to Neumann boundary conditions: u x (0, t) = 0, u x (1, t) = e u(1, t) with convex initial data.